Special relativity and electrodynamics (covariance, metric tensor, field tensor, potentials)

Slides and transcripts: drive.google.com/drive/folder...
TYPO: at 1:06:58, on the left sides of the arrows it should say E_y/c and E_z/c instead of E_y and E_z (so that if beta=0, gamma=1, the expressions are the same on both sides of the arrows).
Many thanks to Henk Bart for providing useful feedback
0:00 Introduction
11:02 Galilean transform
13:45 Lorentz transform (intuition)
21:41 Lorentz transform (mathematics)
27:40 Relativistic mechanics
42:34 Basis transformations: co(ntra)variance
48:20 Metric tensors (general)
50:58 Metric tensor in special relativity
54:23 Covariant/Einstein notation
58:52 Electromagnetism
1:03:25 Transformation of fields (EM field tensor)
1:07:58 Potentials
1:15:18 Retarded time, retarded potentials
1:18:22 Transformation of potentials
1:19:58 Covariant formulation of Maxwell's equations
1:22:40 Importance of symmetries
1:25:05 Summary

[@marshallsweatherhiking1820]

Thank you!!! This is a an amazingly elegant and intuitive first-principles derivation of the famous E = mc^2. Concise but impeccably thorough.

[@sherbajthind3259]

Great Explanation Sir.......

[@charliewu4110]

Beautifully presented. Thank you

[@catmatism]

Glad to have discovered this channel. Subscribed

[@jacobvandijk6525]

Thanks a lot. Inspiring stuff! @ 1:00:25 I'm not a fan of using J, current-density, in the equation for Ampere's law. I favour (dQ/dt)/A (with Q = electrical charge and A = cross-sectional area). It is more consistent with the notation of Faraday's law and with the correction made by Maxwell (both using derivatives with respect to time): 1:01:43. And of course, it's more obvious that we're dealing with changing quantities.

[@weinihao3632]

Thank you very much! It's a gem!

[@NicolasSchmidMusic]

You summarised a whole semester course there ! And it's super well explained and gives a great overview

[@JohnSmall314]

superb

[@NicolasSchmidMusic]

I love you

[@krzysztofciuba271]

OK not completely: at 17:50nn-the typical textbook nonsense on "time dilation". In the "Moving" system (x',t') these parameters x',t' represents not the values "recorded" by the moving "mythical observer=the set of synchronized clocks) but the ones as "been seen" by the observer in the system at rest! The "moving" observer records the same values of x',t' as the stationary observer,i.e., x,t; otherwise, it would violate the 1st Relativity Principle, then also that the unit time (of a clock) and distance (of a "rigid rod") is not "on2=1 sec,ore else)! Consequently, the case of "muon" (as a clock) is the same textbooks BS: a "muon" is a statistical "being=wave packet"; hence, all these experimental data can only be explained if one treats this "muon" as a "wave"; otherwise, the 1/3 of experiments data cannot be counted for -see the diagram for both radioactive "objects" at rest and "moving": in t>T(1/2-a halftime) the values of both functions are almost the same even graphically! One a better exposition of the Subject but not completely again